↑

Properties

Label 5610.bt
Modulus $5610$
Conductor $255$
Order $8$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Downloads

Learn more

Show commands: Pari/GP / SageMath
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5610, base_ring=CyclotomicField(8)) M = H._module chi = DirichletCharacter(H, M([4,2,0,3])) chi.galois_orbit()
 
Copy content pari:[g,chi] = znchar(Mod(287,5610)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(5610\)
Conductor: \(255\)
Copy content sage:chi.conductor()
 
Copy content pari:znconreyconductor(g,chi)
 
Order: \(8\)
Copy content sage:chi.multiplicative_order()
 
Copy content pari:charorder(g,chi)
 
Real: no
Primitive: no, induced from 255.ba
Copy content sage:chi.is_primitive()
 
Copy content pari:#znconreyconductor(g,chi)==1
 
Minimal: yes
Parity: even
Copy content sage:chi.is_odd()
 
Copy content pari:zncharisodd(g,chi)
 

Related number fields

Field of values: \(\Q(\zeta_{8})\)
Fixed field: 8.8.519334883015625.2

Characters in Galois orbit

Character \(-1\) \(1\) \(7\) \(13\) \(19\) \(23\) \(29\) \(31\) \(37\) \(41\) \(43\) \(47\)
\(\chi_{5610}(287,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{8}\right)\) \(i\) \(-i\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(-1\) \(i\)
\(\chi_{5610}(1277,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{8}\right)\) \(i\) \(-i\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(-1\) \(i\)
\(\chi_{5610}(3323,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{8}\right)\) \(-i\) \(i\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(e\left(\frac{3}{8}\right)\) \(-1\) \(-i\)
\(\chi_{5610}(4973,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{8}\right)\) \(-i\) \(i\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{5}{8}\right)\) \(e\left(\frac{1}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(e\left(\frac{7}{8}\right)\) \(-1\) \(-i\)